The topic of this thesis deals with the spiral structure in disk galaxies with a specific aim of probing the influence of the dark matter halo and the interstellar gas on the origin and longevity of the spiral arms in late-type galaxies through theoretical modeling and numerical calculations. The basic theoretical model of the galactic disk used involves gravitationally-coupled two-component system (stars and gas) embedded in a rigid and non-responsive dark matter halo, i.e., the static potential of the dark matter is used in the calculations. However, at places, depending on the nature of the problem addressed, the disk is treated as consisting of only stellar component or only gas component followed by proper justifications for the assumptions. The disk is rotationally-supported in the plane and pressure-supported perpendicular to the plane of the disk. The first part of the thesis involves searching for the dynamical effect of dark matter halo on small-scale spiral structure in dwarf low surface brightness (LSB) galaxies and also some dwarf ir-regular galaxies which host an extended H I disk. In both cases, the rotation curves are found to be dominated by the contribution of the dark matter halo over a large radial distance, starting from the inner regions of the galaxies. The next part of the thesis deals with the investigation of the possible effect of the interstellar gas on the persistence is-sue and the pattern speeds of the spiral structure in the disk galaxies. The last part of the thesis involves in studying the dynamical effect of dark matter halo on large-scale spiral structure. Following is the layout of the thesis. Chapter 1 gives a general introduction to the topic of spiral structure of late-type disk galaxies, followed by a broad overview of the theoretical development of the topic and the present status of the topic. Then the thesis starts with studying the small-scale spiral features and evolves to studying the large-scale spiral features seen in disk galaxies in the following way: Chapters 2 & 3 deal with the effect of dark matter halo on small- scale spiral structure. Chapters 4 & 5 focus on the dynamical effect of the interstellar gas on the spiral structure using the local dispersion relation. Chapters 6 & 7 discuss the possible effect of dark matter halo on large-scale spiral structure in disk galaxies. Chapter 8 contains the summary of results and future plans. Effect of dark matter halo on small-scale spiral structure The spiral arms in the disks of galaxies are often broken into several smaller parts or patches that create a messy visual impression when viewed from a ‘face-on’ configura-tion. They are generally termed as ‘small-scale’ or flocculent spiral arms. Several stud-ies showed that the small-scale spiral arms are basically material arm, i.e., they can be thought of as ‘tubes’ filled with stars and gas. Spiral arms are known to participate in the secular evolution of the disk galaxies. Since disk galaxies are believed to reside within a halo of dark matter, therefore a detailed understanding of possible effects of dark matter halo on the spiral arms is necessary. In Chapter 2, we investigate the effect of dark matter halo on small-scale spiral fea-tures in the disks of LSB galaxies. Modeling the mass distribution within a galaxy from the rotation curve of a typical small LSB galaxy reveals the generic fact that for most of the radii, dark matter halo dominates over the stellar disk. This trend is found to be true from the very inner regions of an LSB disk which in turn makes the LSBs a suitable laboratory for probing the effect of dark matter halo on the dynamics of disk galaxies. Following a semi-analytic approach, and using the observationally measured input pa-rameters for a typical superthin LSB galaxy, UGC 7321, we showed that the dominant dark matter halo suppresses the small-scale spiral structure in the disk of UGC 7321. Since UGC 7321 possesses features typical of a LSB galaxy, we argued that this finding will also hold true for other typical LSBs. The result is at par with the observational evi-dences for the lack of prominent, strong small-scale spiral structure in LSB galaxies. In Chapter 3, we employed the similar techniques for probing the effect of dark matter halo on small-scale spiral structure, except this time we took five dwarf irregular galaxies with an extended H I disk as the sample for our investigation. The main im-portant difference between these dwarf irregular galaxies with the earlier LSB galaxies is that for these dwarf irregular galaxies with extended H I disk, the largest baryonic con-tribution comes from the interstellar gas (mainly H I ), and not from the stars (as seen in LSBs). The extended H I disks of these galaxies allow one measure the rotation curve, and hence modeling the dark matter halo parameters for a large radial range from the galactic center. Here also the rotation curves are found to be dominated by dark matter halo over most of the disk, thus providing yet another ‘laboratory’ for testing the dynam-ical effect of dark matter halo on the dynamics of the disks. Using the observed input parameters for five such dwarf irregular galaxies, we showed that the dense and com-pact dark matter halo is responsible for preventing strong small-scale spiral structure in these galaxies, which is in fair agreement with the observations. Dynamical effect of interstellar gas on longevity of spiral arms Any late-type disk galaxy contains a finite amount of interstellar gas along with the stel-lar component. The atomic hydrogen (H I ) constitutes the bulk of the interstellar gas along with the molecular hydrogen (H2), ionized hydrogen (H I I ), and a trace amount of heavy elements like helium. The mass fraction present in the interstellar gas in disk galaxies is found to vary with the Hubble sequence, with the amount of interstellar gas increasing from Sa type to Scd type of galaxies. Due to the lower value of velocity disper-sion as compared to that of stars, gas is known to have a larger destabilizing effect in the disk. Therefore, the natural question arises about what possible role the interstellar gas could play in the origin and the persistence issue of spiral arms. In Chapter 4, we explored how the interstellar gas could influence the longevity of the spiral arms in late-type disk galaxies by treating the spiral structure as density waves in the disk. The disk is modeled as a gravitationally coupled stars plus gas (two-component) system, where the stars are modeled as a collisionless system and the gas treated as a fluid system. Using the appropriate local dispersion relation for the above mentioned model for the disk of galaxy, we calculated the group velocity of a wavepacket of density wave and then studied the variation of the group velocity with increasing amount of interstellar gas in the system. We showed that the group velocity of a wavepacket in a Milky Way-like disk galaxy decreases steadily with the inclusion of gas, implying that the spiral pattern will survive for a longer time-scale in a more gas-rich galaxy by a factor of few. In Chapter 5, we investigated the role of interstellar gas in obtaining a stable den-sity wave corresponding to the observed pattern speed for the spiral arms. The under-lying local dispersion relation remains same as that is in Chapter 4. Using the observa-tionally measured pattern speed and the rotation curves for three late-type disk galaxies we showed that the presence of interstellar gas in necessary in order to maintain a stable density wave corresponding to the observed values for pattern speeds. Also we proposed a method to determine a range of pattern speed values at any particular radius, corre- sponding to which the density wave can be stable. We applied this method to the same three late-type galaxies which we used in the earlier part of this chapter. We found that, for these three galaxies, the observed pattern speed values indeed fall in the predicted range. Imprint of dark matter halo on large-scale spiral structure Along with the small-scale spiral arms, there also exists another type of spiral arms – the large-scale spiral structure, like what we see M 51 or in NGC 2997, which occupy almost the entire outer optical disk in the galaxy. These spiral arms are termed as ‘grand-design’ spiral structure. One of the competing theories, namely, Density wave theory proposes that the large-scale structure is basically a density wave in the disk and the pattern ex-hibits a rigid-body rotation with a definite constant pattern speed. In the earlier part this thesis (Chapters 2 & 3), it was shown that the small-scale spiral structure gets damped by the dominant dark matter halo. Therefore, a natural question arises whether dominant dark matter plays any role on these large-scale spiral structure; and if yes, to what extent it affects the large-scale spiral structure. In Chapters 6 & 7, we investigated how the large-scale structure in disk galaxies gets affected when the disk galaxy hosts a dark matter halo that dominates over most of the disk regions. We again chose the LSB galaxies as laboratory for this study. In Chapter 6, we modeled the stellar component as a fluid system and in Chapter 7, we treated the stellar system as more realistic collisionless system. In both cases, global spiral modes are identified from the appropriate dispersion relations via a novel quantization rule, and they are used as a ‘proxy’ for the large-scale spiral structure. Using the input pa-rameters for UGC 7321, in Chapter 6 we showed that the fluid representation of stellar system failed to make an impression in suppression of the global spiral modes. However, when stellar component is treated as a more realistic collisionless system, we found that the dark matter halo suppresses the large-scale spiral features as well in the disks of LSB galaxies, in fair agreement with the observations. Finally, in Chapter 8, the thesis concludes with a summary of main results and a brief discussion of the scope for future work.